ﻻ يوجد ملخص باللغة العربية
We study distribution dependent stochastic differential equation driven by a continuous process, without any specification on its law, following the approach initiated in [16]. We provide several criteria for existence and uniqueness of solutions which go beyond the classical globally Lipschitz setting. In particular we show well-posedness of the equation, as well as almost sure convergence of the associated particle system, for drifts satisfying either Osgood-continuity, monotonicity, local Lipschitz or Sobolev differentiability type assumptions.
We study distribution dependent stochastic differential equations with irregular, possibly distributional drift, driven by an additive fractional Brownian motion of Hurst parameter $Hin (0,1)$. We establish strong well-posedness under a variety of as
In this paper, the existence and uniqueness of the distribution dependent SDEs with H{o}lder continuous drift driven by $alpha$-stable process is investigated. Moreover, by using Zvonkin type transformation, the convergence rate of Euler-Maruyama met
We investigate the regularizing effect of certain additive continuous perturbations on SDEs with multiplicative fractional Brownian motion (fBm). Traditionally, a Lipschitz requirement on the drift and diffusion coefficients is imposed to ensure exis
In this paper we study the asymptotic properties of the power variations of stochastic processes of the type X=Y+L, where L is an alpha-stable Levy process, and Y a perturbation which satisfies some mild Lipschitz continuity assumptions. We establish
We prove the unique weak solvability of time-inhomogeneous stochastic differential equations with additive noises and drifts in critical Lebsgue space $L^q([0,T]; L^{p}(mathbb{R}^d))$ with $d/p+2/q=1$. The weak uniqueness is obtained by solving corre